hydrogel thermodynamics (continued) physical hydrogels · pdf filelecture 8 spring 2006 1...

Lecture 8 Spring 2006 1

Hydrogel thermodynamics (continued)Physical hydrogels

Announcements:

Last Day: bioengineering applications of hydrogels

thermodynamics of hydrogel swelling Today: Structure, physical chemistry, and thermodynamics of physical gels Reading: L.E. Bromberg and E.S. Ron, ‘Temperature-responsive gels and thermogelling polymer

matrices for protein and peptide delivery,’ Adv. Drug Deliv. Rev., 31, 197 (1998) Supplementary Reading:

D. Chandler ‘Interfaces and the driving force of hydrophobic assembly,’ Nature 437, 640-647 (2005)


Thermodynamics of hydrogel swelling: Peppas-Merrill theory (derived from Flory-Rehner theory of elastic gels)

Vsswelling

Competing driving forces determine total swelling:

Vr


Chemical potential requirement for equilibrium in the gel:


Governing equation for equilibrium:

( ) ( ) 011 =∆+∆ elmix µµ

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛

++−−=

r

s

r

s

sss

r

sp

C Vv

MM

,2

,2

3/1

,2

,2

2,2,2,2

,21

2,

21

)1ln(21

φφ

φφ

χφφφφ


Example application of Flory-Rehner/Peppas-Merrill theory:

crosslink


Predictions of Flory/Peppas theory

0

20

40

60

80

100

120

0 10000 20000 30000 40000 50000

Mc (g/mole)S

= V

s/

Vd

ry

0.20.10.05

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 10000 20000 30000 40000 50000

Mc (g/mole)

vo

lum

e f

racti

on

po

lym

er

in s

wo

lle

n

sta

te

0.20.10.05

Varying φ2,r:

Q


Predictions of Flory/Peppas theory

Varying χ:

hydrogel swelling vs. solvent quality

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 10000 20000 30000 40000 50000

Mc (g/mole)

vo

lum

e f

rac

tio

n p

oly

me

r in

sw

oll

en

s

tate

0.50.40.2

hydrogel swelling vs. solvent quality

0

20

40

60

80

100

120

0 10000 20000 30000 40000 50000

Mc (g/mole)

S

0.50.40.2

Q


Model parametersµ1

bath chemical potential of water in external bath ( = µ10)

µ1 chemical potential of water in the hydrogel µ1

0 chemical potential of pure water in standard state ∆w12 pair contact interaction energy for polymer with water z model lattice coordination number x number of segments per polymer molecule M Molecular weight of polymer chains before cross-linking Mc Molecular weight of cross-linked subchains n1 number of water molecules in swollen gel χ polymer-solvent interaction parameter kB Boltzman constant T absolute temperature (Kelvin) vm,1 molar volume of solvent (water) vm,2 molar volume of polymer vsp,1 specific volume of solvent (water) vsp,2 specific volume of polymer V2 total volume of polymer Vs total volume of swollen hydrogel Vr total volume of relaxed hydrogel ν number of subchains in network νe number of ‘effective’ subchains in network φ1 volume fraction of water in swollen gel φ2,s volume fraction of polymer in swollen gel φ2,r volume fraction of polymer in relaxed gel


Bonding in physical hydrogels

non-cooperative interactions:

Unstable, no gelation


Bonding in physical hydrogels

cooperative interactions:

Stable interactions, gel forms


Gelation via hydrophobic associations

water

Block sequence controls self-assembled structures formed:


Chemical structure of associative copolymers used in bioengineering

Example blocks:

Hydrophilic B blocks

Hydrophobic A blocks Poly(propylene oxide) (PPO)Poly(butylene oxide) (PBO)

Poly(ethylene glycol) (PEG)

CH3O CH3 O O OHO-(CH-C-O-CH-C-O-)x-(CH2-C-O-CH2-C-O)y-(CH2-CH2-O)z-

PLGA

CH3O CH3 O O O (CH-C-O-CH-C-O-)x-(CH2-C-O-CH2-C-O)y-H

PEG PLGA

PEO PPO PEO


Gelation via hydrophobic associations

Hydroxypropylmethyl cellulose

Poly(N-isopropylacrylamide)

ordered water molecules(minimize water-hydrophobe contacts)R = -CH2-CH-CH3, -CH3, or -H

OHDehydration allows water to disorder (entropically-driven)

∆S = Sdehydrated - Shydrated > 0


Hydrogen-bonded hydrogels


Figures 4 and 5 in Percec, V., T. K. Bera, and R. J. Butera. Biomacromolecules 3 (2002): 272-9.


Ionically-bonded hydrogels

+- Ca++--

Salt bridgeDivalent cations

Alginate(polysaccharide)

+ divalent cations+ cationic polymer

e.g. chitosan (cationic polysaccharide),

polylysine

http://www.lsbu.ac.uk/water/hyalg.html

http://www.lsbu.ac.uk/water/hyalg.html


Combined non-covalent interactions example: coiled-coil peptide gels

Figure 1 in Wang, C., R. J. Stewart, and J. Kopecek. "Hybrid Hydrogels Assembled From Synthetic Polymers and Coiled-coil Protein Domains." Nature 397 (1999): 417-20.

Structure of associating block copolymer hydrogels

Increasing c, T

Hydrophobic block

Hydrophilic block

unimers micelles

‘flower’ micelle

Core-shell micelle



Formation of micelles

Experiments by Hatton group at MIT:

PEO-PPO-PEO micellization at different temperatures measured by adding a hydrophobic dye that absorbs UV light when bound in a hydrophobic environment (e.g. micelle core) but not free in solution

Figure 3 in Alexandridis, P., J. F. Holzwarth, and T. A. Hatton. Macromolecules 27 (1994): 2414-2425.



Intermicelle physical cross-links



5 mm

PEO PPO PEO

Entanglement and H-bonding between packed micelle coronas



Figures 19 and 20 in CCopolymers. Edited by V.

hu, B. and Z. Zhou. Nonionic Surfactants: Polyoxyalkylene Block

M. Nace. New York, NY: Marcel Dekker, 1996, pp. 67-143.


Block length determines gel structure

Figure 14 in Chu, B. Z. Zhou. Nonionic Surfactants: PolyoxyalkyleneBlock Copolymers. Edited by V. M. Nace. New York, NY: Marcel Dekker, 1996, pp. 67-143.


Relation between structure and applications in bioengineering

Cubic phase gel drug depots

Micelle drug nanocarriers

10-50 nmFigure 1 in Zhang, L., D. L. Parsons, C. Navarre, and U. B. Kompella. J Control Release 85 (2002): 73-81.


Thermodynamics of hydrophobic association

T

0 Mole % B 100

T

0 Mole % B 100

UCST LCST

P + S

PS

PS = polymer solutionP + S = two-phase region: polymer-rich, polymer-poor

PS

P + S


Thermodynamics of hydrophobic association


Determination of thermodynamic driving force for triblock self-assembly

Figure 6 and Table 4 in Alexandridis, P., J. F. Holzwarth, and T. A. Hatton. Macromolecules 27 (1994): 2414-2425.


Further Reading

1. Wang, C., Stewart, R. J. & Kopecek, J. (1999) Nature 397, 417-20.2. Guenet Thermoreversible Gelation of Polymers and Biopolymers, New York). 3. Shah, J. C., Sadhale, Y. & Chilukuri, D. M. (2001) Adv Drug Deliv Rev 47, 229-50. 4. Landau, E. M. & Rosenbusch, J. P. (1996) Proc Natl Acad Sci U S A 93, 14532-5. 5. Ron, E. S. & Bromberg, L. E. (1998) Adv Drug Deliv Rev 31, 197-221. 6. Percec, V., Bera, T. K. & Butera, R. J. (2002) Biomacromolecules 3, 272-9. 7. Kuo, C. K. & Ma, P. X. (2001) Biomaterials 22, 511-21. 8. Bray, J. C. & Merrill, E. W. (1973) Journal of Applied Polymer Science 17, 3779-3794. 9. Salem, A. K., Rose, F. R. A. J., Oreffo, R. O. C., Yang, X., Davies, M. C., Mitchell, J. R., Roberts, C. J., Stolnik-Trenkic, S., Tendler, S. J. B., Williams, P. M. & Shakesheff, K. M. (2003) Advanced Materials 15, 210-213. 10. Cao, Y., Rodriguez, A., Vacanti, M., Ibarra, C., Arevalo, C. & Vacanti, C. A. (1998) J Biomater Sci Polym Ed 9, 475-87. 11. Zhang, L., Parsons, D. L., Navarre, C. & Kompella, U. B. (2002) J Control Release 85, 73-81. 12. Jeong, B., Bae, Y. H., Lee, D. S. & Kim, S. W. (1997) Nature 388, 860-2. 13. Chu, B. & Zhou, Z. (1996) in Nonionic Surfactants: Polyoxyalkylene Block Copolymers, ed. Nace, V. M. (Marcel Dekker, New York), pp. 67-143. 14. Chu, B. (1995) Langmuir 11, 414-421. 15. Alexandridis, P., Holzwarth, J. F. & Hatton, T. A. (1994) Macromolecules 27, 2414-2425.

hydrogel thermodynamics (continued) physical hydrogels · pdf filelecture 8 spring 2006 1...

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